Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

using i64 = int64_t;
const i64 MOD = 1e9 + 7;
const i64 INF = i64(1e18) + 7;

signed main(){
    int N;cin >> N;
    vector<double> vec;
    for(int i = 0;i < N;i++){
        int a;cin >> a;
        vec.push_back(a);
    }
    double ans = -1e9;
    sort(vec.begin(), vec.end());
    for(int i = 0;i < N-1;i++){
        for(int j = i+1;j < N;j++){
            int cnt = 0;
            double sum = 0;
            for(int k = N-1;k >= 0;k--){
                if(cnt >= 2)break;
                if(i == k || j == k){
                    continue;
                }else{
                    cnt++;
                    sum += vec[k];
                }
            }
            ans = max(ans, sum / (vec[j] - vec[i]));
        }
    }
    cout<<setprecision(20)<<ans<<endl;
}